A “peanut gallery” is the top balcony of a theater—the cheapest seats with usually the furthest views of the stage, and where the crowd often got rowdy. The term “peanut gallery” is cited in print from at least 1867.
 
The popular snack in the “peanut gallery” is peanuts—a snack often thrown at the stage. Stage lecturers often warned against “comments from the peanut gallery.” Peanuts are not as popular a snack as they once were and the term “peanut gallery” is dated, but is still used.
 
A 2018 post on StackExchange: English Language & Usage suggests another “peanut gallery” meaning:
   
“Whatever it may be now, ‘peanut gallery’ seems to have started as a thin veneer laid over more overtly racist names for segregated seating.”
   
   
Wikipedia: Peanut gallery
A peanut gallery is an audience that heckles the performer. The term originated in the days of vaudeville as a nickname for the cheapest (and ostensibly rowdiest) seats in the theater; the cheapest snack served at the theater would often be peanuts, which the patrons would sometimes throw at the performers on stage to show their disapproval. The phrases “no comments from the peanut gallery” or “quiet in the peanut gallery” are extensions of the name.
 
In the late 1940s the Howdy Doody show adopted the name to represent their audience of 40 kids.
 
Related terms
. In Europe the claque at many opera houses and theatres were an organized group who would (and in Italy still may) cheer performances hysterically or boo and cat-call, depending on the outcome of financial negotiations between their leader and the lead performers’ agents.
. Similar seats in British theatres are often called “the gods” because of the seats’ higher elevation (e.g., “We’ve got seats in the gods for the play tonight”).
. Similar seats in French theatres were called “le paradis” (from which came the title of the movie “Les Enfants du Paradis”) because of the seats’ higher elevation. Another common name was “le poulailler” (the henhouse) because the population of the section was very noisy.
. In the US and Canada, especially at sporting events and concerts, the more elevated seats are often referred to as “the nosebleeds”, alluding to the altitude.
. During the Jim Crow era and in segregated parts of the United States, “nigger heaven” was often used to refer to the balcony of a movie theater where blacks sat.
. The orange-colored seats in the upper decks of Three Rivers Stadium in Pittsburgh were often referred to by local patrons as “Peanut Heaven.”
. A section of elevated seats at Miller Park in Milwaukee, Wisconsin are referred to as “Uecker Seats.”
 
Dictionary of American Regional English
peanut gallery n scattered, but chiefly east of Missip R See Map Cf peanut heaven, peanut roost, DS D40
The top balcony of a theater.
 
(Oxford English Dictionary)
peanut gallery n. colloq. (freq. depreciative) the top gallery in a theatre or cinema, usually the location of the cheapest seats and hence regarded as the most vocal or rowdy section of the audience; also in extended use.
1876 Mountain Democrat (Placerville, Calif.) 10 June 2/1 As a bid for applause from the political pit and *peanut gallery it was a masterpiece.
a1877 E. H. KNIGHT Pract. Dict. Mech. III. 2476/2 The syrinx was used by the Romans as a noisy improvement on hissing… The occupants of our peanut galleries, however, use it indiscriminately for praise or blame.
1945 New Yorker 5 May 15/1 We were sitting in the peanut gallery of the Opera House.
1988 R. CARON Jojo i. 7 Chip..had plenty of encouragement from his private ‘peanut gallery’ of retired oldsters who sat day after day on a flat bench in front of the garage.
 
16 January 1867, The Daily Picayune (New Orleans, LA), “Academy of Music,” pg. 2, col. 1:
It is useless for us to repeat our praises of Johnny Thompson, Billy Reeves, and others of the company, as negro delineators; they “out Herod Herod,” and put the darkies in the “peanut gallery” fairly to the blush.
       
30 January 1869, The Weekly Nonpareil (Council Bluffs, IA), “The Women in Council,” pg. 2, col. 1:
The virtuous pride and swelling indignation with which this costacular imputation of Parson Gray was spurned must have been amusing to the small boys in the peanut gallery.
 
28 June 1869, Brooklyn (NY) Daily Eagle, pg. 2, col. 6:
PLYMOUTH ORGAN CONCERTS: The Concert of Saturday was a fitting close to the first season of these eminently successful entertainments, the like of which in all respects we have never had in Brooklyn before, and which we may add cannot be too freely imitated. The church was crowded in every part,—including even the third tiers of seats which the boys irreverently call the “Pea-nut Gallery.”
   
24 August 1871, The Daily National Republican (Washington, DC), “Knights Templar,” pg. 4, col. 1:
As we could not make the doorkeepers or ushers understand, we were thrown upon our own resources, and finally obtained seats in the highest part of the theatre, (peanut gallery,) which was found was about as fashionable as any other part of the house.
 
1 December 1871, Philadelphia (PA) Inquirer, “Henry Ward Beecher,” pg. 1, col. 1:
The “Peanut” gallery, which occupies a position near the ceiling, is likewise a jam.
 
Google Books
Europe Viewed Through American Spectacles
By Charles Carroll Fulton
Philadelphia, PA: J. B. Lippincott & Co.
1874
Pg. 53:
Whilst waiting, one of the speculators offered us three seats on the fourth bench in the fifth gallery for fifty florins, or over eight dollars apiece, but, concluding that we could see nothing worth seeing from this position, in what we would call the “peanut gallery” at home, we respectfully declined the proposal.
 
9 April 1874, New Orleans (LA) Times Picayune, “Les Miserables,” pg. 6:
Only five or six indictments were filed, among which there was one for carrying a concealed weapon, although Sam could hardly be said to carry a concealed weapon, as he displayed it pretty freelyt, flourishing it around his head, in the manner in which he learnt from the pea-nut gallery in the theatre was the custom of Captain Jack and his Modocs.
 
10 April 1874, St. Albans (VT) Daily Messenger, pg. 3:
The manager of the New Orleans Varieties Theatre stood dumbfounded in the august presence which approached him one evening during Mardi Gras and asked for a front seat, and a sure sight at Salvini. (...) “My dear sir, excuse me! I should as soon think of putting General Grant in the peanut gallery as deny you a front seat in this theatre.”
 
15 January 1875, Jamestown (NY) Journal, pg. 6:
Yet with all these capillary improvements, one looks down from his seat in the peanut gallery on a sea of bald heads—shining pates.
 
15 May 1875, Inter Ocean (Chicago, IL), “Vassar,” pg. 5:
In the college for gentlemen there is always a back seat, which is to the lecture room what the peanut gallery is to the theater, a place devoted to the sleepy and rowdy element, who lounge and whittle and wish the bell would ring.
 
Google Books
April 1897, Kansas University Quarterly, vol. 6, no. 2, “Dialect Word-List - No. 4” by W. H. Carruth and Paul Wilkinson, pg. 90:
peanut heaven: the highest gallery in a theatre.—General.
   
Penn State Daily Collegian (May 24, 1969)
So much for comments from the peanut gallery.
       
Google Books
When Children Think:
Using Journals to Encourage Creative Thinking
By Gabriel H. L. Jacobs
Published by Teachers College Press
1970
Pg. 8:
No comments from the peanut gallery please. 
 
Google Books
One Wizard Place
By D. M. Paul
Published by Doug Paul
2008
Pg. 130:
“Shush… no comments from the peanut gallery.”
 
StackExchange: English Language & Usage
Whatever it may be now, ‘peanut gallery’ seems to have started as a thin veneer laid over more overtly racist names for segregated seating.
(...)
In isolation, the use of ‘peanut gallery’ in The Times-Picayune of 1867 might be considered incidental to the skin tones of those seated there; it is not in isolation, however. The same section of seats was commonly called the ‘negro gallery’ (from at least 1853 to the mid-1900s), the ‘nigger gallery’ (from at least 1860 to the mid-1900s), and the ‘nigger seats’ (from at least 1833). For example, this early use of ‘nigger seats’ lays the practice and terminology bare:
(...)
answered Jan 26 ‘18 at 5:09
JEL